Mathematics of Finance from Udemy

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Syllabus

Compound Interest

In this video you will be introduced to common terms used in the theory of interest such as present value, future value, annual interest rates, and periodic interest rates. You will also learn the main compound interest formula.

After watching this video you will have a better understanding of the compound interest formula and the different terms that appear in it. You will know how to calculate the future value of an investment and the interest earned.

After watching this video you will know what an effective rate is and how to calculate it. You will be able to use the effective rate to compare two different investments (with different rates and compound frequencies), to find out which investment is the better choice.

After watching this video you will be able to figure out how much to invest so that it grows to a specific value in the future for a given interest rate.

After watching this video you will know how to find the interest rate which will grow your investment to a specific future value over a specific length of time.

After watching this video you will be able to find the length of time it takes for some initial principal to grow to a specific future value under a given interest rate.

After watching this video you will understand what it means for interest to be compounded continuously. You will also learn about a famous mathematical constant called Euler's number and will find out its relationship to compound interest.

After watching this video you will understand the main formula for interest compounded continuously. The formula is derived in this video.

After watching this video you will be able to calculate the effective rate for interest compounded continuously. You will be able to use it to compare investments.

After watching this video you will know how to solve for time in the formula for interest compounded continuously. You will also learn to solve for the nominal rate. Therefore you will be able to calculate the length of time for an investment to grow to a specific amount when interest is compounded continuously. You will also know what rate is required so that an investment grows to a specific amount in a fixed amount of time when interest is compounded continuously.

In this video we quickly review the main concepts and formulas in the previous videos.

After watching this video you will know what an annuity is. We talk about the difference between an ordinary annuity and an annuity due. You will also understand what the present value and future value of an annuity are. We do not introduce any new formulas in this video.

In this video we define what a geometric series is and find a formula for its sum. This formula is necessary for finding the present value and future value formulas for annuities. This formula only gets used in the next two videos which are derivation videos. If you want you can skip this video as well as the next two if you are not as interested in the math behind the formulas. It will give you a better understanding of the material though.

In this video we derive the future value formula for an ordinary annuity. If you want to skip this video and just see how we use the formula later then that is fine.

In this video we derive the present value formula for an ordinary annuity. If you want to skip this video and just see how we use the formula later then that is fine.

After watching this video you will know what the present value and future value formulas are for an ordinary annuity. You will also know some common finance notation which gets used when using these formulas.

After watching this video you will be able to calculate the future value of an ordinary annuity.

After watching this video you will be able to calculate the present value of an ordinary annuity. This video is a continuation of the example from the previous video.

After watching this video you will know the present value and future value formulas for annuities due. In this video we only derive the formulas so feel free to skip to the next video where we show how to use them.

After watching this video you will be able to calculate the present value and future value for annuities due.

After watching this video you will be able to calculate different quantities related to the amortization of loans. You will be able to calculate the periodic payment, the outstanding principal, the interest in a specific payment, the principal contained in a specific payment, and the total interest paid.

After watching this video you will know what it means to amortize a loan. You will also learn five different amortization formulas. These formulas will be used in an example in the next video.

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Explores compound interest, annuities, and loan amortization, which are fundamental concepts for understanding investments, savings, and debt management

Covers effective rates, enabling learners to compare different investment options with varying rates and compounding frequencies, which is crucial for making informed financial decisions

Includes derivations of formulas for future and present values of annuities, which may be skipped by learners less interested in the mathematical theory behind the formulas

Examines interest compounded continuously and Euler's number, which provides a deeper understanding of advanced financial calculations and mathematical concepts

Details the amortization of loans, enabling learners to calculate periodic payments, outstanding principal, and interest, which is essential for understanding loan structures

Reviews summary

Fundamentals of finance mathematics

According to learners, this course provides a solid foundation in the mathematics of finance. Students report that the lectures offer clear and concise explanations of core concepts like compound interest, annuities, and loan amortization. The material is often described as easy to follow and well-structured, making it suitable for beginners looking to understand basic financial calculations. While some reviewers note that mathematical derivations are included, they appreciate that these sections are optional and not essential for applying the main formulas. The course is viewed as a great starting point for understanding the quantitative aspects of personal or business finance, although a few mention it may lack the depth required for more advanced financial analysis.

Deeper math included but optional.

"I liked that the geometric series part was there for understanding, but wasn't mandatory."

"You can skip the derivation videos if you just want to learn the formulas."

"Found the math derivations a bit tough, but thankfully they weren't needed for the problems."

A solid introduction to the math.

"This is a perfect course if you are new to the math behind finance."

"Provides a solid foundation for understanding basic financial calculations."

"I had no prior finance math background, and this course got me up to speed quickly."

"Great starting point, but you'll likely need more advanced courses later."

Concepts are explained well and clearly.

"The instructor explains everything very clearly, especially the concepts of compound interest and effective rates."

"I found the videos on annuities easy to follow and the formulas well presented."

"Everything was laid out logically and explained simply. Great for a beginner like me."

"The math is broken down step-by-step, making complex ideas understandable."

Focuses only on fundamentals.

"Excellent for basics, but doesn't cover investments or complex financial products."

"Good intro, but don't expect advanced topics or portfolio theory here."

"I was hoping for more depth on valuation or derivatives, but it sticks to the core."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mathematics of Finance with these activities:

Review Algebra Fundamentals

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Strengthen your understanding of core algebraic concepts. A solid foundation in algebra is crucial for grasping the formulas and calculations used in finance.

Browse courses on Exponents

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Review key concepts like exponents, logarithms, and equation solving.
Work through practice problems to reinforce your skills.
Identify areas where you need more review.

Read 'The Total Money Makeover' by Dave Ramsey

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Gain a practical understanding of personal finance principles. This book complements the mathematical concepts by providing real-world applications and strategies.

View Build a Business You Love: Mastering the Five... on Amazon

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Read the book and take notes on key concepts.
Reflect on how the concepts relate to the course material.
Consider how you can apply these principles to your own finances.

Calculate Compound Interest Scenarios

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Reinforce your understanding of compound interest calculations. Practice applying the formulas to different scenarios to improve your accuracy and speed.

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Find compound interest practice problems online.
Solve problems with varying interest rates, compounding periods, and timeframes.
Check your answers and review any mistakes.

Four other activities

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Explain Annuities to a Friend

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Test your understanding of annuities by explaining the concept to someone else. Teaching others is a great way to reinforce your own learning.

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Prepare a simple explanation of annuities.
Explain the different types of annuities and their uses.
Answer any questions your friend may have.

Build an Amortization Schedule

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Solidify your knowledge of loan amortization. Creating a schedule will help you visualize how loan payments are allocated between principal and interest over time.

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Choose a loan amount, interest rate, and loan term.
Use a spreadsheet program to create the amortization schedule.
Calculate the periodic payment, interest, and principal for each period.
Verify that the loan is fully paid off at the end of the term.

Analyze Mortgage Options

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Apply your knowledge of loan amortization to a real-world scenario. Compare different mortgage options to determine the best choice for a given situation.

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Research different mortgage options available in your area.
Gather information on interest rates, loan terms, and fees.
Use the formulas learned in the course to calculate the total cost of each option.
Compare the options and determine which is the most favorable.

Read 'The Intelligent Investor' by Benjamin Graham

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Gain insights into investment strategies and risk management. This book provides a broader context for the mathematical concepts covered in the course.

View Melania on Amazon

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Read the book and highlight key concepts.
Reflect on how the concepts relate to investment decisions.
Consider how you can apply these principles to your own investments.

Career center

Learners who complete Mathematics of Finance will develop knowledge and skills that may be useful to these careers:

Actuary

An actuary analyzes risk and uncertainty, often working for insurance companies or financial institutions. This role requires a strong understanding of financial mathematics, and this course in the Mathematics of Finance provides a solid foundation for that. Actuaries need to understand compound interest, annuities, and loan amortization, all of which are covered in detail in this course. In particular, the sections on effective rates, present value, and future value calculations would be useful. Aspiring actuaries may find that this course helps them prepare for the actuarial exams often required for professional certification.

See salaries and explore the career path for Actuary

Financial Planner

A financial planner helps individuals manage their money and achieve their financial goals. This Mathematics of Finance course provides knowledge of the fundamentals of financial mathematics, including compound interest, annuities, and loan amortization, which are all crucial for creating effective financial plans. The concepts of understanding present and future values, as covered in this course, would be useful for forecasting investment growth and retirement savings. By taking this course a financial planner will be able to analyze various investment strategies and advise clients.

See salaries and explore the career path for Financial Planner

Loan Officer

A loan officer evaluates and approves loan applications for individuals and businesses. Understanding loan amortization, a core topic in this Mathematics of Finance course, is critical for this role. The course also covers the mathematics behind interest rates and payment calculations. A loan officer needs to understand the intricacies of loan structures and payment schedules. The course's coverage of principal and interest calculations helps loan officers understand the financial implications of lending. This course may provide a background in how interest is applied to loans.

See salaries and explore the career path for Loan Officer

Financial Analyst

A financial analyst evaluates investments and provides recommendations to businesses and individuals. This course in the Mathematics of Finance may be useful because it covers key concepts like compound interest, annuities, and loan amortization, all essential for analyzing financial products and making informed investment decisions. Knowing how to calculate present and future values, as taught in this course, is crucial for determining the worth of various investment opportunities. The section on continuous compounding may prove particularly helpful, as well.

See salaries and explore the career path for Financial Analyst

Underwriter

An underwriter evaluates and assumes risks for insurance companies or financial institutions. The Mathematics of Finance course covers financial concepts like compound interest and loan amortization. Underwriters need to understand risk and financial implications. By taking this course, an underwriter establishes a foundation of financial knowledge. This can be particularly useful for understanding the terms and conditions of financial products.

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Treasury Analyst

A treasury analyst manages a company's cash flow and investments. This Mathematics of Finance course would provide a critical introduction to the mathematics underlying corporate finance, including the management of debt and the valuation of investments. The course covers concepts like compound interest and annuities. A treasury analyst needs to have a strong understanding of financial calculations. The course's sections on present value, future value, and effective interest rates are particularly relevant.

See salaries and explore the career path for Treasury Analyst

Credit Analyst

A credit analyst assesses the creditworthiness of individuals or businesses. This Mathematics of Finance course may be useful because it offers education on the mathematics of finance, specifically compound interest and loan amortization, which are directly relevant to credit risk assessment. The course helps build a foundation of how interest accrues and how loans are repaid. Therefore this course is valuable for those who wish to be credit analysts.

See salaries and explore the career path for Credit Analyst

Budget Analyst

A budget analyst helps organizations manage their finances by developing and monitoring budgets. This Mathematics of Finance course may be helpful because it provides a strong foundation in understanding financial calculations, particularly those related to compound interest and annuities, which are relevant to long term forecasting. Budget analysts need to be able to project future costs and revenues. The course's sections on present value and future value calculations are helpful in budgeting. This course is helpful for understanding financial modeling.

See salaries and explore the career path for Budget Analyst

Investment Banker

An investment banker helps companies raise capital by issuing stocks and bonds. Although an investment banker typically requires an advanced degree, this course could provide a foundation for further study. To succeed, an investment banker must have a grasp on the time value of money, which is covered in the Mathematics of Finance course through its modules on compound interest and annuities. The course's detailed explanations of present value and future value calculations could be a significant benefit. This is not a replacement for an MBA or related degree, but could provide a useful background.

See salaries and explore the career path for Investment Banker

Commercial Real Estate Agent

A commercial real estate agent helps clients buy, sell, or lease commercial properties. A commercial real estate agent needs an understanding of financial mathematics, particularly regarding mortgages and property valuation. This course in the Mathematics of Finance can help expand your understanding of financial principles. Agents need to understand how interest rates affect property values as presented in the compound interest section. Such knowledge may be valuable for assessing the financial viability of real estate investment opportunities.

See salaries and explore the career path for Commercial Real Estate Agent

Portfolio Manager

A portfolio manager makes investment decisions on behalf of clients. This role typically requires an advanced degree. This Mathematics of Finance course would provide a foundation for understanding the financial aspects of portfolio management, including investment valuation and risk assessment. A portfolio manager must have an understanding of compound interest and annuities, as taught in the course. The knowledge of present value, future value, and continuous compounding gained from this course may be helpful. Although a portfolio manager generally holds a master's degree, this course can help.

See salaries and explore the career path for Portfolio Manager

Real Estate Appraiser

A real estate appraiser estimates the value of properties. This course in the Mathematics of Finance would provide a foundation for understanding the financial aspects of real estate, particularly in calculations related to mortgages and property valuation. The loan amortization module of this course may be helpful, and the real estate appraiser uses these skills when working with mortgages. Appraisers need to understand how interest rates affect property values, as presented in the compound interest section. Such knowledge may be valuable for assessing the financial viability of real estate investments.

See salaries and explore the career path for Real Estate Appraiser

Accountant

An accountant prepares and analyzes financial records. This course may be useful because it provides a strong foundation in financial mathematics, covering topics like compound interest and loan amortization. Accountants need to grasp how interest accrues and how loans are repaid. The Mathematics of Finance course offers a great introduction to these topics. The sections on present value and future value calculations may be particularly relevant. By taking this course, accountants can improve their understanding of financial transactions and reporting.

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Management Consultant

A management consultant advises organizations on how to improve their performance and efficiency. While this role often requires an advanced degree, this Mathematics of Finance course may be useful for understanding the financial implications of different business strategies. The course's coverage of compound interest, annuities, and loan amortization could provide a basis for making financial recommendations. Management consultants benefit from understanding present value and interest rates. This is not a replacement for a business degree, but could be helpful.

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Economist

An economist studies the production and distribution of resources. This generally requires an advanced degree. Knowledge from this Mathematics of Finance course may be helpful for economists who focus on financial markets or investment analysis. Economists need to create models based on assumptions, and creating useful assumptions in finance requires a solid base of knowledge. The course's coverage of compound interest and annuities may provide valuable knowledge of these areas. Although economists typically have a master's or doctoral degree, this course could be a plus.

See salaries and explore the career path for Economist

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Mathematics of Finance.

Build a Business You Love

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Provides a practical guide to personal finance. It covers topics like debt management, saving, and investing. While not strictly mathematical, it provides a real-world context for the concepts learned in the course, particularly regarding loans and annuities. It is best used as additional reading to provide context.

Build a Business You Love: Mastering the Five...

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Mathematics of Finance

What's inside

Syllabus

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Reviews summary

Fundamentals of finance mathematics

Activities

Career center

Reading list

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